On a Clear Day …

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On a Clear Day . . .Doris Glass

As the sun rises over the hills my com-panion and I see the moon sinking intothe sea. Today will be two minutes long-er than yesterday. The sun may be whatkeeps the living alive, but didn’t themoon make first life possible? Was itthe surging swirl of sea water in the tidepools that brought about that strangemix of mud�the right triumverate ofpressure, volume and tempera-ture�that was on the threshold of thedoor to life? And behind the tide hidesthe moon.

Sir John TennielArlist

’The time has come.’ ihe Walrus said,

’To link of many things:Of shoes�and ships�and sealing \\’ax-

()f cabbages�and A’ings�

Through the Looking Glass

by Lewis CarrollAs we descend the ramp to the beach I

recall Julius Sumner Miller’s introduction to his delightful little book:

All of a half-century ago, when I was a little boy on the farm in my native New Eng-land, I remember asking all kinds of questions. What is the earth made of? Why is thesky blue? Why is the sunset red? How does a bird soar? Why does a brook gurgle? Howdoes an earthworm crawl? Why is a dewdrop round? Why does corn pop? Why does awood fire crackle? And a thousand like questions. To a few I got the answers in reading.To some I got the answers in dialog with my mama and papa and with my teachers.Some: thought out�not too well, to be sure�but I was learning to think. By this de-vice�ever questioning, ever uncertain�I gathered up a rather massive body of knowl-edge.

Years ago, as students, we learned about Newton and the apple�how earth’sgravity pulls the apple to the ground, and how he was the first to realize that themoon was pulled by the earth the same as the apple. And now some of us teachthat. If we do, we have already made a mistake�sown a weed seed that will growas we cultivate the garden of the mind�because earth’s gravity is but half thestory. Isn’t it just as much the apple’s gravity? Are you thinking, "But the apple

School Science and MathematicsVolume 86 (2) February 1986

On a Clear Day 157

is so small."? Now we are at the core of Newton’s apple! The meek shall inheritthe earth. The key question is: Which pull is greater, the pull of the earth on themoon, or the pull of the moon on the earth? But all this is not my point!My point is: How to answer a question that Julius doesn’t mention in his

beautiful introduction�a question often asked in science classrooms. "Whydoesn’t the moon fall to earth like the apple? Why does the moon stay upthere?" The standard answer found in conventional textbooks is, "Ah, but themoon does fall! It falls from where it would have been if it didn’tV’ Procrusteanplaying with wwds?� worthy of *Humpty Dumpty? And the student is toomuch puzzled to say anything more.Would it help to say, "The moon doesn’t stay ’up there’�it stays up, but it

doesn’t stay thereV"] Let’s face it. Linear motion is easy to describe and explain;rotary motion is hard. And most texts (teachers too?) take up too much timewith linear, and then have to skip over rotary.High tide, 5.4 feet at 6:37 AM had left its mark on the sand�a buffet for the

birds as I began our matutinal dialectic."A science textbook should be judged by the way it explains the tides.""Why? It seems simple enough. The moon attracts the water, pulling it into a

bulge. Right?" My companion’s gaze was steady on my face."Not quite. It isn’t easy to make it simple and tell the truth. The moon does at-

tract the water,�and the water attracts the moon just as much.""Isn’t that a bit picky?"" ’Little drops of water, tiny grains of sand, make the mighty ocean and the

pleasant land.’ It was a trivial distinction years ago, but not now. The art ofscience�and mathematics�includes knowing what is, and when it is, negligibleor trivial. Locally, we say ’ground level,’ and draw a horizontal line, but theearth is not flat. It is curved," I said."What are you talking about? What has that got to do with the tides?""The core of the apple: How do you explain the bulge on the other side of the

earth? Tide is not diurnal, you know! We set the trap when we teach that the ac-celeration of gravity is constant."

"Didn’t Galileo observe the two bodies of different mass dropped from thetower strike the ground at the same time?"

"Yes, but he dropped them from the same/;eight.91"So�? Would that have made any difference?""No. No measurable difference. But Newton discovered that the closer the

bodies the stronger the gravity pull, and the stronger pull means more accelera-tion.""And the tidal bulge on both sides of the earth?""There are four bodies on a line�water, earth, water, and moon. The water

on the moon side is pulled more than the earth, and the earth is pulled more thanthe water on the other side. That’s all," I responded.


158 On a Clear Day

"Slow down a bit. You’re walking�and talking�too fast. Is the high tide thesame height on both the near and far sides of the earth? And what about the ef-fect of the moon revolving?�and the earth rotating?"

Humpty Dumpty is the human egg that had a great ’fall* inThrough the Looking Glass by Lewis Carroll;"When / use a word," Humpty said, in rather a scornful

lone, "it means just what I choose it to mean�neither morenor less.""The question is," said Alice, "whether you can make

words mean so many different things.""The question is," said Humpty Dumpty, "which is to be

master�that’s all."Alice was too much puzzled to say anything.

"Now^oi/Stalking too fast. All that takes time and a better place."So should we say that we saw the sunrise and the moonset?�or, instead, that

we saw the earth turn? Consider well the words of Theodore Andrea Cook:

So I have emphasized the importance of divergencies, or discrepancies, because theyset us hunting after sequences of events that have hitherto remained unnoticed or un-known.We sometimes speak of exceptions or of things abnormal because they are phenome-

na which manifest their obedience to some special law unknown to us. In reality nothingis abnormal. We must be ready, in every scientific investigation, for occurrences whichmight, in a narrow view, be called exceptions^ but which in reality provide an indicationof the presence of some other principles conditioning the whole of our original hypothe-sis. It has long been recognized that no theory whatever can represent absolute truth. Alaw, in the sense in which I use it here, obviously expresses an ideal condition underwhich certain results occur in given circumstances. Such circumstances never occur inreal life.

But science would never progress unless experiments were constantly revealing dis-agreement between laws and facts. This means that we have only arrived at the formula-tion of a law by so far doing violence to Nature as to isolate the problem we wish tostudy, by eliminating as many factors as we believe may complicate the question. This isas much as to say that a law only approximates to the facts; and every time we use it wehave to make appropriate additions or corrections. Laws had no existence until we for-mulated them, and they cease to exist when we have merged them in a wider, a morefundamental, principle. They neither express reality nor are they real themselves. Theyare the instrument of science; not its aim.

Can we rely on mathematics to keep us on a straight and narrow path? Wouldyou like to see an example of how mathematics not only does not help butharms? Consider that old familiar catechismal formula for the distance (space)traveled by a body under constant acceleration: s = ’/2at2. How do we explainthe ’one-half’?�and the ’square’? Be prepared for a surprise!


On a Clear Day 159

THE TIDEThe tide rises, the tide falls,The twilight darkens, the curlew calls;Along the sea-sands damp and brownThe traveler hastens toward the town,And the tide rises, the tide falls.

Darkness settles on roofs and walls,But the sea, the sea in the darkness calls;The little waves, with their soft, white hands,Efface the footprints in the sands,And the tide rises, the tide falls.

The morning breaks; the steeds in their stallsStamp and neigh, as the hostler calls;The day returns, but nevermoreReturns the traveller to the shore,And the tide rises, the tide falls.

Henry Wadsworth LongfellowWhat do you think?

Doris Glassc/o Editor, School Science and Mathematics

*Editor’s Note:Humpty Dumpty is the human egg that had a great Tall* in Through the LookingGlass by Lewis Carroll:"When /use a word,’* Humpty said, in rather a scornful tone, "it means just

what I choose it to mean�neither more nor less.""The question is," said Alice, "whether you can make words mean so many

different things.""The question is," said Humpty Dumpty, "which is to be master�that’s all."Alice was too much puzzled to say anything.

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